Lee Hwa Chung theorem

Lee Hwa Chung theorem—Let M be a symplectic manifold with symplectic form ω. Let α be a differential k-form on M which is invariant for all Hamiltonian vector fields. Then:

• If k is odd, α = 0.
• If k is even, ${\displaystyle \alpha =c\times \omega ^{\wedge {\frac {k}{2}}}}$, where ${\displaystyle c\in \mathbb {R} }$.